Sampling Designs Proportionate to Non-negative Functions of two Quantiles of Auxiliary Variable

Estimation of the population average in a finite population by means of sampling strategies dependent on sample quantiles of an auxiliary variable are considered. The sampling design proportional to an order statistic of an auxiliary variable was defined by Wywiał (2007, 2008). It was generalized into case of the sampling design proportional to the difference of two order statistics by Wywiał (2009), too. In this paper those results are generalized on the case of a conditional sampling design. Several strategies including the Horvitz-Thompson statistic and regression estimators are considered. Their accuracy is analyzed on the basis of computer simulation experiments.